An important part of prospecting, drilling and developing oil fields is the construction of 3D geologic models of the subsurface stratigraphy (hereinafter 3D surface models). This can be done by collecting 3D data points that represent points on stratigraphic surfaces below the ground. The 3D data points may come from data collected during the drilling of wells in the region, or from other scientific evidence of the existence of surfaces below the ground. When building the 3D surface models from 3D data points, various constraints can be placed on the algorithms used to interpolate and extrapolate the 3D data points into the surfaces. One such constraint is the requirement for geologic conformance. For example, a surface that was deposited on top of a previously existing surface can often be said to conform to the earlier surface. It could also be said that the previously existing surface conforms to the later surface. Such a relationship implies that the two surfaces will not intersect each other when building a 3D surface model. It may also imply that a map of the distance between the two surfaces will obey some simple mathematical rule, such as possessing a minimum curvature.
One method for modeling 3D surfaces that are related in this way is to first build one of the surfaces (either the upper or the lower) using only the 3D data points that are thought to intersect that surface. The 3D surface built first is known as the constraining surface in the relationship. Then, the 3D data points of the second surface (known as the constrained surface) are transformed to a thickness domain by transforming the z values into vertical distances from the constraining surface. The 3D data points in the thickness domain are used to build a 3D surface model that represents the thickness between the two surfaces, which is also known as a thickness map. Finally, the constrained surface is built by adding the values for the nodes on a solution grid representing the 3D surface model to the z values for the constraining surface that will yield a 3D surface model of the constrained surface in the z domain. Because the 3D data points of the constrained surface are not taken into account when the constraining surface is built, the constraining surface may be built both above and below the 3D data points of the constrained surface leading to a thickness map with both positive and negative thicknesses. In other words, the constrained surface overlaps (intersects) the constraining surface in the z domain. The resulting overlap does not conform to the known geologic condition that the two surfaces were laid down by sedimentation in a stratigraphic sequence.
Other methods for modeling 3D surfaces attempt to prevent the constrained surface from overlapping the constraining surface either by requiring the thickness map to be built with all positive or all negative values (i.e. by imposing a global unilateral constraint on the thickness map) or by building the constrained surface after the constraining surface is built and imposing each node value of the constraining surface as a maximum or a minimum limit on each respective node value of the constrained surface (i.e. by imposing unilateral node constraints on the constrained surface). However, such methods may result in the constrained surface not intersecting some of the 3D data points that are thought to intersect it.